How then do you know you are getting the maths right if you can't see what it represents?No one understands QM at a "intuitive" level.
Like I say you get used to it.How then do you know you are getting the maths right if you can't see what it represents? All of my thought processes depend on some sort of visual feedback to let me know that I am going in the right direction. Without it I get lost.
What do you think about Hawton's position operator? (see e.g. http://arxiv.org/abs/quant-ph/0101011) At the end of his FAQ entry, Neumeier criticizes that this operator isn't compatible with Lorentz invariance although Hawton has published a paper claiming the contrary in Phys. Rev. A (http://arxiv.org/abs/0804.3773).A photon cannot be "localized" in a strict sense. One cannot even define a position operator in the strict sense for massless particles with spin [itex]\geq 1[/itex].
The quantity E+iB is called the Riemann-Silberstein vector. For a short overview of its use in both QM as well as classical physics, see http://arxiv.org/abs/1211.2655. You also find a couple of articles mentioning it if you search the arxiv for "photon wave function".Kith, can you quote a source for this particular equation?
No one understands QM at a "intuitive" level.
Even though this is certainly correct in some sense, my impression is that such statements are often used to dismiss questions about the basics of QM which could improve one's understanding greatly. One example is the question about the complex nature of the wavefunction. The links to continuous transformations and generalized probability theories which allow for entanglement, for example, are quite recent achievements. Although the complex nature of the wavefunction can be traced back to these plausible fundamental principles, I often hear answers like "that's just how QM works", "no one really understands QM", "you just have to get used to QM's rules", etc. to this question. If people like Lucien Hardy hadn't followed their dissatisfaction with such answers, we would know a lot less about the foundations of QM.You simply get used to it.
Many people only care about the rules. In order to solve a physical problem you always have to find an appropriate model. Although physics strifes for unification, you don't use the most fundamental model but the most simple one. Physicists are used to using different models for different situations without a practical need to relate these models.What is your secret?
That's true.If people like Lucien Hardy hadn't followed their dissatisfaction with such answers, we would know a lot less about the foundations of QM.
By working out solutions for situations that people have studied before, and comparing them to experimental results, or to already generally-accepted solutions. Gradually you develop a feel for it, and you gain confidence in applying it to new situations. As Bill said, "you get used to it."How then do you know you are getting the maths right if you can't see what it represents?
To compliment f95toli's reply, there is a pair of books which make an attempt, and a pretty decent one, to make the mathematics of QM more plain and concrete. They also give a relatively accessible approach to understanding the derivation and application of QM math:Otherwise, how else can you understand this stuff? What is your secret?